Distributed constrained optimization for multi-agent networks with nonsmooth objective functions

This paper investigates the distributed constrained optimization problem in multi-agent systems, where agents cooperatively minimize an objective function being the sum of each agent's objective function while meeting equality and inequality constraints. By virtue of nonsmooth analysis and graph theory, a novel distributed continuous-time algorithm is proposed to solve such a kind of optimization problems. Different from existing continuous-time results relying on the differentiability or strict (strong) convexity of local objective functions, the proposed approach considers more general local objective functions which are only convex and not necessarily smooth. In addition, the proposed approach considers more general local constraints, not just box constraints considered in most existing studies. The optimality of the proposed algorithm is ensured under certain initial condition. Based on set-valued LaSalle invariance principle, the convergence of the proposed scheme is rigorously proved. Finally, simulation examples are applied to validate the effectiveness of the proposed algorithm. (C) 2018 Elsevier B.V. All rights reserved.